Tap chi Khoa bpc BHQGHN: Nghien cihi Giao due Tap 30, S6 212014) 19-27
Nghien curu cac tinh hudng day hpc Toan trong moi tnrong may tinh bo tui nha mot phan mem gia lap
Le Thai Bao Thien Trung
Khoa Todn-Tin, Trudng Dgi hoc Suphgm TP. Hd Chi Minh, 280 An Dirong Vuong, qugn 5. TP. Hd Chi Minh. Viet Nam
Nhan ngay 20 thang 3 nam 2014
Chinh sira ngay 18 thang 4 nam 2014; chap nhan dang ngay 25 thang 6 n5m 2014 Tom t3t: Trong chircmg trinh va cac sach giao khoa pho thong Viet Nam hien hanh, xu huong sir dung may tinh bo tui (MTBT) de trg giup tinh loan va to chiic cac hoeit d^ng giang day Toan ngay cang dugc khuyen khich. Van de ihiet ke cac tinh huong day hoc Toan co sif dung MTBT va thuc nghiem danh gia cac hoat dong nay nhim hoan thien chiing truac khi ap dung vao thuc te giang day doi hoi phai co nhung nghien cihi nghiem tiic ca ve phuong dien ly luan lin thirc nghiem. Tuy nhien, cac nha nghien cihi phircmg phap giang day Toan thieu mot phuang tien de thu diap thong tin khi trien khai cac tinh huong day hoc voi MTBT. Trong bao cao nay, chiing t6i se gidi thieu mpt phan mim gia lap (PMGL) co giao dien cua loai MTBT dang dugc su dung pho bien a nha trucmg pho thong hien nay de thu thap thong tin ve cac thao tac bam may ciia hgc sinh {theo mo hinh may tinh Alpro cua Nguyen Chi Thanh 2005, [7]). Chung toi ciing sg giai thieu va phan lich mot tinh huong day hoc co sit dung MTBT. Kiln thiic nhim d6n trong tinli huong nay la do chinh xac ciia kit qua trong mot nhiem vu tinh gan diing.
Tir khda: Day hpc Toan, may tinh bo tin, phan mem gia lap, tinh gan dung.
1. L i d o xay d y n g m o t p h a n m e m gia l a p Trong cdc sach giao khoa (SGK) pb6 thong Viet Nam hiSn hanh, viec sii dung M T B T de thuc hien cac tinh toan va to chuc cac hoat-dgng day hgc da dugc minh hga mgt each cbinh t h u c ' . Su xuat hien manh me ciia M T B T dat ra vin de nghien curu anh h u o n g ciia chiing v a each thirc tich hgp chiing trong day hgc Toan.
Chiing ta hay xem xet mgt kieu sai lam quen thugc dugc tim thay trong bai lam c u a n h i l u hgc sinh lien quan den bai loan khao sat
DT 84-909657826 Email: letbttrung@gmail com
' Vol lo^i mSy CASIO FX-220MS (cho b?ic hpc THCS) v.
CASIO FX-500MS (cho b^: hpc THPT).
ham so va ve do thi a cac ki thi tot nghiep trung hgc ph6 thong (THPT) v a tuyen sinh cao d i n g , dpi hgc. Chang han, vdi yeu cau khao sat v a vS do thi ciia ham so
= / M =
-x'-5x'+llx+l.f(x) = 2x^-10x+12 = Bang bien thien:
0 ' » x = 3hayx = 2
X
f(x) Sx)
-oo 3 2 + i » + 0 0 -
~ • ^ — - ^
L TB. T- Trung Tgp ehi Khoa hpc DHQGHN: Nghien ein< Gido d{ic, Tgp 30. S6 2 (2014) 19-27
Su nhim lln thii to ^ua bai nghiem ciia dgo ham tren bang biln thien xu5t hien kha pho bien trong cac bai Iam ciia hgc sinh^ Vay, dau la nguon goc ciia sai ISm ti-en?
Mgt yeu to tra Iai cho cau hoi thii nhiit co thi dugc tim thdy khi chiing ta thuc hien lai viec tim nghiem ciia dao ham bang chirc nang giai phuang trinh bac hai mgt an cua may CASIO FX 570MS (loai may tinh ph6 biln hien nay trong nha truong Viet Nam).
Nbu vay. thii tu xuat hien cac nghiem cua MTBT giai thich cho sai lam ve m|t thijf tu ciia cbiing tren true so ciia bang bien thien. Nha nghiSn ciiai se de phat hien nguyen nhan sai ISm ban khi hp co m6t cong cu de xem lai diln bien thyc td ciia hgc sinh khi su dung MTBT.
Trong boi canh dat ra, chiing toi nhan thay sg can thiet phai xay dung mgt PMGL co giao dien va hanh vi so gidng vdi cSc loai MTBT dugc su dyng pho bien trong truang pbo thong Vi|t Nam hi?n nay"\ PMGL la mgt cong cu cho ph6p tiep c|n "/i(5p den"* - nguoi bgc - a cac
" Sai lam iren xuSt hien ngay ca khi hoc sinh tinh fl;3) va f(2) trong bang bien thifin. Viec ve dung d6 thj (voi bang bien thien sai) trong tradng h^p nay cho thay duong nhu hgc sinh dl thupc cac d^ng do ihj iing vcri cac dang ham sd quen thugc trong day hoc giai tich.
' Chung toi da chgn giao dien va hanh i i s6 ciia MTBT CASIO FX570 MS Ak xay dung P.MGL Wang ung - loai may dang dugc hgc sinh tnmg hpc su dyng pho bien hifn naj',
* "Cho den giiia the ki XX nguoi ta vin tin ring, niu kliong CO each gl hieu sau duoc tam linh con nguoi. thi cfing CO nhu:ng quy luat chung chi phoi each img xir ciia timg ci the.
I-l Tic nhan kich thieh S > Chii th^
> Phan \^ dap lai R
(Hgp den)
tinh huong day hgc cu the trong moi trudng MTBT nho chiic nang luu lai cac phim ma hgc sinh da thao tac.
BAD cAo
PMGL CO chuc nang lim lai cac phim da thao tac va cac ket qua tinh toan tuong iing ma nguai hgc da thuc hien tren giao di?n MTBT CLia PMGL. Nghta la, neu chi quan sat san pbSm viet ciia hgc sinh trong nhieu hoat dgng day hpc vdi MTBT, cbiing ta sg khong biet ro dieu gi dan den cau tra Iai ciia hg ciing nhu dieu
^ khien hg khong tra Iai. Chiing toi se Iam ro hem nhung lgi icb ke tren trong pbSn tilp theo ciia bai bdo.
Chiing toi da van dung PMGL dl nghiSn cim bai tinh bufing day bgc Toan lien quan den cac chti de: so gan diing va lap trinh tinh toan.
Trong khuon kho ciia bai bao nay, chiing toi chgn gidi thieu truong bgp d^iy hgc tinh toan gan diing.
2. Nghien ciiii mgt boat dgng d^y hgc vo'l phan mem gia l^p: t r u ^ g bgp s6 gan diing
Trong hau hit cac nganh nghe dugc dao tao a bac cao dkng - dai hgc, nguoi hgc it nhieu deu phai thuc hien cac tinh toan gSn diing. Nhung chi mgt so it trong sd cac nganh hgc a bac nay con nghifin ciiu sau vl s6 gin diing. Vi vay, ngu6i hgc chi dua chii yeu vao c^c kiln thiic da tiep thu 6 b$c ph6 thong khi thuc hi^n cac phep Trong quan diem nay, chu the duoc coi nhu mgt hpp den.
Nguoi ta kh6ng tinh gi dSn ljch su, kien thuc, quy trinh tu duy cua chii the" ([1], trang 39).
L. T B. T. Trung / Tt^ chi Khoa hoc DHQGHN • Nghiei u Gido due. Tap 30. So 2 (2014) 19-27
tinh gan diing. Sinh vien thuang dat cau hoi;
chiing ta phai ldy bao nhieu chu so thap phSn?
Cau hdi nay chac chan se lam nhieu giang vien Iiing tiing va kho dua ra cau tra Iai hgp li va nhu vay cac cau hoi Toan hgc sau day co the dugc dat ra:
- Tai sao phai lam tron ket qua gan diing tir MTBT?
- Lam sao xac dinh do chinh xac ciia mgt ket qua gdn diing nay? Lam sao cai thien no?
2.7. Mdt sdyiutd Todn hgc vi ddi tuong sd gdn dung
Trong khuon kho ciia bai bao, chiing toi chi tong hgp Iai mgt s6 khia canh cdn thiet vl ddi tugng sd ^ n diing nham giai Hiich va danh gia thuc trai^ day hgc d6i tugng nay a truong ph6 diong. (Thiing toi ciing gioi han nghien ciiu cua minh tren s6 ^ diing tiiap phan, dugc sir dung gan nhu duy nhdt trong cac tinh toan thong thuong.
Khi udc luong mgt so thuc bang mgt so gan diing ma khong danh gia dugc do chinh xac thi so gan diing dy khong co gia tri su dung, Noi each khac mgi so deu la so g ^ diing ciia nhau va van de la so nao gan voi so can tim hon.
D8 danh gia mgt so gan diing, ta thuang dinh nghTa khai niem sai sd tuyit ddi:
"Neu a* Id gid tri dung cua mgt dgi lugng vd a la gid tri gdn diing ciia a* thi sai sd tuyet ddi cua gid tri gdn diing a Id dai lugng Aa sao cho |a*-aj<Aa . Vgy a-Aa<d*<a+Aa. Ta thudng ghi: a* = a ± A a ". ([6]. Irang 13).
Diing truoc yeu cau can udc luong mgt so nao do ta di tim so gan diing va can phai danh gia s6 gan diing nay nghTa la Iai phai uoc lugng sai so tuyet doi. Thuat ngir do chinh xdc dugc hilu la mgt udc lugng ciia sai s6 tuyet d6i.
Ching ban, sai so tuyet doi cua 1,41 - mgt so gdn diing ciia-^ - dugc bieu dien hinh thiic la
| ^ - 1 . 4 | . Tuy nhien, bieu dien hinh thuc na\
chang cho biet dugc do chmh xac ciia sai so.
Vay la, ta lai can phai tinh gan dung |V2-1,41|.
Noi each khac, pbai bdng long vdi mgt Aa sao cbo |>^-1,4I| nho nghiem ngat ban Aa. chdng han|>/2-I,4I|<I0-l
Gicri ban trong van de xap xi thap phan, khi thirc hien tinh toan gan diing nguai ta thuong hai long chgn mgt ket qua thap phan theo quy tdc ldm trdn va trong truang hgp nay mgt do cbinh xac co the khong dugc thong bao tuong minh. Quy tac Iam tron co the dugc phat bilu nhu sau:
"[...] quy trdn sao cho sai sd quy trdn tuyet ddi khdng ldn hon mdt nira dan vi d hdng dugc giir lai cudi cimg, tuc Id 5 don vi d hdng bd di ddu tien, cu thi Id. niu chu sd bd di ddu lien > 5 thi them vdo chir sd giir lai cudi cimg mdi don vi, cdn niu cha sd bddi ddu tien <5 thi de nguyen chir sd g}ir lgi cuoi cirng". ([9], trcmglO).
Nhu vay, quy tdc nay dugc ap dung tren mgt khai trien th|p phan ciia so thtrc. Cbiing ta se danh gia dugc sai so tuyet doi khi Iam tron so va nhu vay xac dinh dugc mgt do chinh xac.
Chang ban ngutri ta thuang viet V5=i;2,2361 nhung khong noi ro do chinh xac, theo tinh chat da phat bi^u, 2,2361 co sai so tuyet doi nho hon hay bang 0,5.10"* va mgi cbii- so thap phan cua so gan dung nay deu la chir sd chdc chdn .
Cach viet so gan dung dang a •=^ a,a^a2..^„
khong kem theo do chinh xac co the khien nguai ta hieu nhdm: mgi chir so ciia no deu la cha so chdc chan nghia la no co mgt do chinh xac 0,5.10"" hay don gian hon no co mgt do chinh xac 10". Cach hieu nay sai khi chiing ta thuc hien nhilu tinh loan gdn dung trung gian nhung lai khong danh gia sai so tuyet doi ciia so cuoi ciing thong qua cac sai so trung gjan.
Cba so thap phan thii k dupc goi la chfi so cbSc chan oeu Aa< —.10* voi Aa la sai so tuyet doi cua so gan dung a ciia so thuc a*.
LT.B-T Trung/Tgp chi Khoa hgc DHQGHN- Nghien ciru Giao due. Tap 30. 562(2014) 19-27
Khong khd dl chiing minh quy luat don gian ve sai s6 d6i vai hai phep toan cgng va tru:
Khi thuc hien phep cgng hay trir tren moi cap s6 gan diing co cimg so chii so thap phan, gia su CO n chii so thap phan. vdi dieu kien mgi chii so ciia chiing deu chac chan thi ket qua nhan dugc chi dam bao n-I chir so thap phan dau tien la chdc chan.
Tuy nhien, quy luat vl sai s6 d6i voi phep nhan hay chia cac c3p so thap phan phuc t^p hon nhieu va phu thugc vao i> le giiia sai so va dO Ion ciia cac so thap phan trong pbep tinh.
Khai niem sai sd tuang ddf co thi dugc sii dung d£ nghien ciiu sai so trong cac phep tinh nhan va chia.
2 2. Sd gdn dung trong day hgc Todn bgc trung hgc
Cac npi dung lien quan true tiep den tri thiic ve s6 g ^ diing dugc giang d^y o lop 7 (bac trung hoc CO so) va lop 10 (bac tmng hgc pho thong).
Myc tieu giang day so gan diing dugc neu trong chuang trinh Toan 7 (trang 97) nhu sau:
- Ve kl nang, hgc sinh phai "van dung thanh ihgo cdc quy tdc ldm trdn sd".
- Ve kien thirc, hgc sinh "biet y nghTa ciia viec ldm trdn so " vdi ghi chii "khdng di cdp den cdc khdi niem sai sd tuyit ddi, sai sd tuang ddi, cdc phep Todn ve sai sd ".
Chiing ta cd the dat cau hoi: nlu khai niem sai so hoan toan khong dugc de c ^ den 6 lop 7 thi nhiing y nghia nao ma he thong day hpc co thi mong dgi o nguai hgc doi vdi viec lam tron s6?
Chiing toi khong tim thdy mgt Ii do nao tit phuong dien Toan hgc ciing nhu thuc tl giai thich cho cac quy tac Iam tron so khi xem xet SGK Toan 7 - ngbta la: khong c6 li do cho cSu hdi tai sao phii lam tron s6. D6i voi hpc sinh sau, viec lam tron so tii mgt so thap phan cho truoc duang nhu cbi mang y ngbta nhu su viet ggn so thap phan nay kem theo dau w.
Chuong trinh Toan 10 (trang 34) dat ra myc tieu:
- Ve kt nang, hgc sinh "viit duge so quy trdn dya vdo dg chinh xdc cho trudc " va "biet sir dung mdy tinh bo tiii de linh lodn vdi cdc so gdn ddng".
- Ve kien thiic, hgc sinh "biet khai niem so gan diing, sai so".
Su xuat hien ciia hai doi tugng co ban gdn vdi khai niem so gan diing - sai so va do chinh xac - hira hen lam rd y nghia ciia cac quy tdc lam tron ma hgc sinh da dugc yeu cau thuc hi^n thanh thao a Lap 7. Ngoai ra, MTBT tro thanh cong cy duy nhat giiip khai trien th^p phan cac s6 thuc cr b^c hgc nay. Chang h?in:
"4 Thve hi^ ph^ tinh sau irin mdy luift ba rui (trong kit qvd ldy 4 cMt s6 afA\Bn ihap
Hitting dm each gidi cau a) Niu dung may tmh CASIO ft-500 MStalam nhu sau
An lien ttip phim |MQP£] cho din khi mdn hinh hifn i F H Sci N o n n
An li^ li^^^di 1^- 4 c t e id d'phdn thgp phdn. Kit qua Idat ra trht mdn lmh U 8183.004^ {[101 XiJ3)
Sai so tuong doi ciia a - gia trj gan diing eiia a' - la lupng Sa sao cho —<^ga
LT-B.T. Trung Tgp chi Khoa hoc DHQGHN: Nghien ciru Gido due. Tap 30, 56 2 (2014) 19-27
Tuy nhien, viec dgc ket qua khong dugc giai thich bang cac tri thiic toan hgc ve so gan diing da giang day.
Den day, ta co thi kit luan: hgc sinh dugc mong dgi sir dung quy tdc lam tron khi dgc cac ket qua tinh toan gdn diing tii man hinh MTBT nhung khong can giai thich ^ ve d6 chinh xac ciia cac ket qua nay tir cac khai niem sai so tuyet doi hay do chinh xac da gidi thieu.
Vai trb cong cu cua so gdn dung trong dgy hgc Todn b&c trung hgc
Sau khi doi tugng so gan diing dugc n ^ e n cuu o Ldp 10, no tro thanh cong cu trong cac bai toan tinh gdn dung sau do. chdng h^n tinh gan dung dien tich, thi tich va giai lam giac...
Chiing toi gidi han nghien ciiu cua minh trong lop bai toan giai tam giac (trong ngi dung Hinh hgc Ldp 10) vi a do viec tinh gan diing dugc thuc hien nhieu nhdt voi myc dich: xet xem cac khai niem co ban gan voi doi tugng so gan diing nhu sai s6 tuyet ddi va do chinh xac dugc van dung nhu the nao.
Trong chii de Giai tam giac, hpc sinh dugc cho phep va mong dgi tbuc bien cac tinh toan gan diing. Nguoi hgc se giai ma dieu na\ thong qua viec cac so do canh co don vj. chang ban nhir "cm" va goc co don v i " ° ". Vi du:
"Cho lam gidc ABC cd .^=120". cgnh b=8cm vd c= Scm. Tinh canh a vd cdc gdc B, C:'([ll],tr59)
Sau da} la Ien ^ai mong dgi trong sach giao vien:
^Theo dinh li cdsin lo c6.
: .: ..: ..A li „ .
Tuy nhien neu ta tinh true tilp goc B theo cong diirc g = i:-os"'(—••"'"^ —) voi gia tri
2ac chinh xac a" = 129 bdng MTBT ta co:
. ( ( 1 2 9 + 5 5 - 8 2 ) : |
2nc 2.1L?6.5 . B - ? - ^ 4 g - [ . . . r a i 2 L t r 6 8 )
Nghia la hai chii so thap phan sau dau phay tir ket qua ciia SGV khong phai la cac chu s6 chac chan.
Tat ca de bai toan giai tam giac trong hai quySn SGK Hinh hgc Lop 10 (co ban va nang cao) deu thi^u quy dinh ve do chinh xac ciia cac ket qua can tinh. Cac ket qua gan diing trinh bay trong bai ^ai dugc dgc tir man hinh hien thi ket qua thap phan cda MTBT bang quy tdc Iam tron nhung khong he chi ro do chinh xac.
Ngoai ra, viec tinh gan diing ket qua cuoi ciing dugc thuc hien thong qua cac ket qua g^n diing trung ^an va dieu nay lam cho cac chir so cua ket qua cudi cimg kbong con dam bao la cac chfi so chdc chdn nua. Noi each khdc ta hoan toan khong biet do chinh xac ciia ket qua can tim.
2.3. Nghien ciru mgt iinh hudng dgy hoc nhd phan mem gid lap
Chiing toi da xay dung, phan tich va thuc nghiem mgt tinh huong day hgc xoay quanh mgt bai toan thugc kieu ti'nh toan cac ylu t6 ciia tam giac vuong kha quen thugc trong chuong trinh THCS. Muc tieu ciia thyc nghiem la tao ra mgt moi truong cho phep b6 sung cho hgc sinh hai ket luan sau:
- Ket luan I: Neu thirc hien tinh gdn dung ihdng qua cdc sd gdn dung cd dugc tir cdc linh lodn trimg gian thi do chinh xdc d cdc budc trung gian se dnh budng den do chinh xdc d budc cudi cimg.
- Ket luan 2: Muon cd dd chinh xdc tdt han, ta chi thuc hien tinh todn gdn dung d budc cudi
L TB.T Trung Tgp chi Khoa hge DHQGHN: Nghien cuu Gido due. Tdp 30. S6 2 (2014) 19-27
ciing vdi MTBT. Nghia la thiel Igp mdt quy trinh hay mgt cdng thuc tinh todn true tiip kel qud vd thay sd vdo birdc cudi cimg.
Tinh hudng g6m 3 pha diln ra trong 45 phiit xoay quanh bai toan:
Cho tam giac ABC vuong tai C, AC = 55,9808 cm; AB=57,9556cni. Tren AB lay M sao cho MA-— AB. N la diem tren c^inh AC 2
3
sao cho MN vuong goc vcri AC. Hay tinh do dai MN (chinh xac den 4 chu s6 thap phan sau dau phay).
Chiing toi chgn lira nhiJng s6 do voi bon chO' s6 thip phan (khac vdi cac ket qua gan diing trong sich giao khoa: thuang la mgt hay hai chii so thap phan) voi muc dich cho hgc sinh tinh gan diing voi do chinh xac cao. Bdi vi, nhilu tinh todn gan diing trong kinh te va khoa hgc kl thuat yeu cau nhiing kit qua co sai sd rdt nho. Ngoai ra, khi thuc hi?n nhieu tinh toan trung gian, neu dg cbinh xac chi khoang 10'^
(iJTig vdi h^ chu so th|ip phan) s^ sd de xay ra vdri phan nguyen ciia ket qua.
Trong khudn khd ciia bai bdo, chiing tdi chi trinh bay pha I ciia tinh hudng va lam rd lgi ich ciia PMGL trong viec phan tich san phdm thyc nghiSm.
20 hgc sinh ciia mgt lop 12 (da hpc xong cdc ndi dung ve sd gdn diing va giai tam gidc) dugc yeu cdu md PMGL tren cac may tinb di§n tu va
^ai bai toan tren (nghta la tinh gan diing MN chinh xac din 4 chii sd th^p phan sau ddu phdy).
Vdi nhiing lua chpn cho bai toan, ta co the du kiln hai nhdm chien luge gidi nhu sau :
- Nhdm chiin luge 1: Tinh gdn dung ihdng qua cdc kit qua gdn dung trung gian Hgc sinh thuc hien cac tinh toan gdn diing a budc trung gian va sii dung cac kit qua gan diing a buoc trung gian de tinh MN.
Trong tnrdng hgp nay ta cd tbi du kiln mdt sd kit qua quan sat dugc nhu sau:
Ket qua I : tinh MN = — BC theo gij tri gan dung cua BC 2 3
BC = 4AB--AC- =^57,9556=-55,9808= «15,0001 AW = - B C « 1 0 , 0 0 0 1
3
K^t qua 2: tinh h/lN — \1AM~ — AN' theo cac gia trj gan diing ciia AM va AN
-J T 2 AM-- A B - - 57,9556=38,6371. A\= - AO37,3205
3 3 3 MN=4AM'- AN- =10.0003
Ket qua tir man hinh MTBT 2 J 3 X 1 5 . & 0 0 1 •
IDDGODBBBl
Ket qua tCr man hinh MTBT
. 2 - 3 7 . 3 2 0 5 2 ) •
- Nhdm chien luge 2- Chi tinh gdn dung d hudc cudi ciing
Chiing tdi hy vgng su xudt hien chien luge nay vi su thuan lgi khi su dung djnh li Thales.
Trong trudng hgp nay, chiing ta cd thi quan sdt thay mdt sd ket qua nhu sau:
I
L.TBT. Trung f Tgp chi Khoa hoe DHQGHN- Nghien ciiu Gido dye, Tgp 30, So 2 (2014) 19-27
K £ t q u a 3 : t i n h .W = - J C = -^/.tf•-.^C' 3 3
ilS- = -BC = -iiS--.4C- =-j57,9556=-55.9808= =10,0000 3 3 3 ^
K i t qua 4: Tinh MN = M-ABf-(-AS)-
MN= = J ( - X 57,9556)= - ( - X 55,9808)= =10,0000
Ket qua tir man hinh MTBT
. i - 5 5 . 9 S & 8 2 ) -
(00000356?
Ket qua tir man hinh MTBT
. X 5 5 . 9 6 9 ^ ) 2 ) -
W0BD3SB^
Neu nhip diing cii phap vao MTBT thi nhdm chien luge nay c6 thi cbo kSt qua chinb xac den 4 chii sd tb^p phan sau dau phay ludn la 10,0000.
Sau pha I ta cd the td chiic mdt sy ddi chieu giiia cac ket qua khdc nhau do 2 nhdm chien luge mang l^ii va tiln banh tdng kit thanh cac ket iuan trong pha 2 va pha 3.
Chien luge
Ket qua quan sat diroc
Tinh gdn dung Ihdng qua cdc kel qud gdn diing trung gian 10,0003 hay 10,0001 hay, v.v...
Chi linh gdn diing d hudc cudi cimg
10,0000 hay 10
Ket qud thuc nghiem pha 1 vd lgi ieh cua PMGL
- Phii hgp vdi ket qua phan tich chuang trinh SGK, chiing tdi ghi nhan 18 (tren 20) hgc sinh su dung chiln luge tinh gan diing thdng qua cac kit qua gdn diing trung gian. Chdng han:
BAO CAO
- Vdi su lira chgn ciia bai toan, chiing ta c6 2 (tren 20) hpc sinh sii dyng chien luge chi tinh gan diing d budc cudi cung. Chang han:
BAO CAO
EOIIBSKB03SM-X • S ! S M = » - Chiic nang luu I?i lich sir bam phim cua PMGL cho phep chiing tdi quan sat nhimg ket qua khac (chua du kiln dugc trong phan tich tien nghiem) ciia chien luge tfnh gdn dung thdng qua cac kit qua gdn diing trung gian.
Chdng ban:
BAO CAO
MN
Hgc sinh ma MAxBC
27 da tinh AB thdng qua gia tri gan diing
f2^rQj][SC[qEiSI3 7
vdi 4 chu s6 thap phan sau dau phay ciia BC=I5,000I va AM=38,637I. Nhu v^y nha nghien ciiu se biit ro li do tai sao cd ket qua gan diing cua MN la 10,0001.
- Nlu khdng c6 PMGL chiing tdi se khd xac dinh hgc sinh dS sii dyng chien luge nao. Bdi vi
L TB T. Trung.' Tgp chi Khoa hgc DHQGHN: Nghien cini Giao due. Tgp 30, So 2 (2014) 19-2 7
cung dudi su anh hudng ciia cac SGK mdt sd hgc sinh khdng de y den yeu cau lay 4 chu" sd thap phan sau ddu phay va mac dii su dung chiln luge tinh gan diing thdng qua cdc ket qua gan diing trung gian hg vdn cho ket qua MN * 10. Chdng ban:
BAO CAO
cua BC" gdm 8 chii sd thap phan sau ddu phay*.
Nho vay ma BC cd do chinh xac cao nhu khi tinh true tilp BC d hgc sinh mS s6 21 (15,00005342). Tuy nhien hgc sinh dS cdt sd cua ket qua gan diing BC va sii dung MN khi
, , , ^ , MAxBC ^_
tmh MN = — — . Cung nhu hgc sinh mi sd 21, hgc sinh ma sd 01 Iai tinh dugc kit qud Id 10.
B1131~IEsl"iIZ .
Hgc sinh ma sd 21 da tinh MN- BC 3/2 gia trj gan diing ctia BC la 15 do cdt tir ket qua 15,00005342 hien thj tren man hinh MTBT.
- Chiing tdi cdn phdt hien su sir dung phim nhd Ans' d mpt sd bpc sinh. Vi?c mot sd hgc sinh sii dung phim nhd nay md ra trien vpng day hgc cdc yeu to lap trinh vdi MTBT da dugc phan tich rd trong Nguyen Chi Thanh (2005).
BAO CAO
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wummEKwimm 38£IIDSEE}__
^u'3iMmsmmwm\cmmmm e
That thii vj khi phan tich Idi giai nay cua hgc sinh ma sd 01 ma chdc chdn chiing ta se khdng nhin thay dugc neu chi dua vao san pham viet ciia em. Tiln trinh tinh loan ciia hgc sinh nhu sau:
Tinh gdn diing BC^ = AB^ - AC". Bdng cdch su dung phim nhd Ans, hgc sinh da tinh gdn diing BC thdng qua VAUS , nght la tinh gdn diing BC vdi phep khai can tir gia tri gdn diing
3. Thay cho kit luan
Viec nghien cuu cac tinh hudng d?y hpc Toan vdi MTBT nhd su giiip dd ciia PMGL da cho thay nhiing lgi ich quan trgng ciia PMGL da tbilt kl trong vile pban tich cdc san phdm cua ngudi hgc. Tu quan dilm ciia trudng phd!
Didactic (Phap) ve gid thuyet hgc t|p, chiing ta cd the lam rd su ddng hod vd dieu iing trong qua trinh hgc bang each tu thich nghi ciia ngudi hgc.
"Chu the hoc bang cdch tir thich nghi (dong hda vd dieu ung) vdi mgt mdi trudng gdy ra nhirng mdu thudn, khd khdn, su mdt cdn bdng".
([I], trang 53).
Viec tinh den tinh trang kien thiic cua hpc sinh thdng qua cac phan tich chuong trinh va SGK se cho phep thilt kl mgt hoat dgng d?y bgc hpp Ii trong mdi trudng MTBT. Bin lugt minh, PMGL cho phep quan sat dl dieu chinh va cai tien cdc boat ddng dgy hgc nhdm giiip
Phim nho na_\' lim lai kei qua tinh toan cuoi cimg vira duoc tlnic hi^n thanh cong
* Tham khao Le Thai Bao Thien Tmng (2010): tuy mSy tinh CASIO lx570MS chi hiSn thj ^ i da 10 chO s6 th?p phan (tinh ca tnrctc va sau dau phay ) nhung no luon tinh loan vol 11 cha so th^p phan (co mot cha $5 tfa^p phin cuoi cung khong hiln thi tren man hinh). Trong tinh toin cua hpc sinh 21, kit qua hien thj tren man hinh III 225,0016027 ghi co 7 chu: so th^p phan sau d^u ;Aay.
Nhung khi hoc sinh ggi phim nho Ans, ket qua gan dung dugc sir dyng trong tinh loan tidp theo la 225.00160272 gom 8 chit so thSp phan sau dau phay (ban dpc c6 the kiem tra b§ng each lay Ans trir cho 225.0016027 sS thay ChQ sd 2.10"^).
LTB.T Tnmg Tap chi Khoa hoc DHQGHS Nghie u Gido due Tap 30, So 2 <2014) 19-27
ngudi bgc tu thich nghi dl tilp thu mgt each tich cue cdc tri thiic toan hgc cdn day.
Tai lieu tham khao
II] A. BessoL C. Comili. Le Thj Hoai Chau. Le Van Tlcn. Nhiing yeu Id ca ban cua didactic loan (£lements fondamentaux de didaclique des mathematiques) - Sach song ngC Vi^-Phap.
NXB DHQG Thanh phd H6 Chi Minh. 2009.
[2] A. BirebenL Articulation entrc la caiculatrice et r^proximation decimale dans Ies calculs numeriques de Tenseignement secondaire fran?ais: choix des calculs trigonometriques pour line ingenierie didaclique en classe de Premiere scientifique. These. Universite Joseph Fourier - Grenoble 1.2001.
[3] B9 Gi&) dye va Oao t ^ , Chuong uinh Toan pho thdng. NXB Giao dye. 2007.
[4] Le Thai Bao Thien Trung. Notion de limite et decimalisation des nombre reels au lycee.
ISBN: 978-613-1-51572-9. N"XB Universitaire Europ^nnes.2010.
[5] Le Thai Bao Thien Trung, Van de img dung cdng ngh? thdng tin trong dgy hpc Toan va cac
lgi ich cua may tinh cam tay. Tap chi Khoa hoc Giao due s6 30 (64). DHSP TPHCM. thang 9 nam 2011.
[6] Nguyen Chi Long. Phucmg p h ^ tinh. NXB Dai hoc Qu6c gia TP. H6 Chi Minh. 2003.
[7] Nguyen Chi Thanh, La notion d'algoridime et de programmalion dans lenseigncment au Kcee et au debut de rUniversite. These en cotutelle a TEeole Norraale Suf>erieurc n°l de Hanoi et a I'UJF. 2005.
[8] Phan Diic Chinh (Tdng diii bien). Ton Than (Chu bien), Vu Hihi Binh. P h ^ Gia Dire, Tran Luan. Toan 7 (tap I), NXB Giao due. 2008.
[9] Ta Van Diiih. Phuong phap tinh. N"XB Grao dye. 2003.
[10] Tran Van Hgo (T6ng CM Uen) - Vu Tuan (Oiii bien) - l > m Minh Cuong - Do Manh Himg - Nguyin Ti&i Tai D^ so 10. NXB Giao dye. 2007.
[11] Tran Van Hao (Tong chu bien). Vii Tuin (Chu bien), Doan Minh Cuong. Do Manh Himg. Nguyin Tien Tai, Hinh hpc 10, NXB Giao due, 2006.
[12] Tran Van Hao (Tong chii bien), Vu Tuan (Chii bien). Doan Minh Cucmg. D6 Mgnh Hiing.
Nguyen Tien Tai. Hinh hoc 10 (Sach giao vien).
NXB Giao due, 2006.
Study on Mathematics Teaching Situations m the Calculator Environment with a Software Emulator
Le Thai Bao Thien Tnmg
Mathematics and Computer Science Faculty, Pedagogical University of HCM City, 280 An Duang Vucmg, District 5, Hd Chi Minh City, Vietnam
Abstract: In the current program and text books for secondary education in Vietnam, the tendency to use the calculator to help calculate and organize math teaching activities has been ever more encouraged. But the design of maths teaching situation with the use of "calculator" and the experimental evaluation in order to perfect them before ^plying them to the teaching realities demand the serious studies both in the theoritical and practical aspects. However, the researchers of the maths teaching method lack a facility to collect information to implement the teachnig situations with the calculators. In this report, we present a software emulator with the interactive of the calculator being used widespread in the secondaiy schools now so as to collect information on the manipulation of the keys by students (according to the model of caculator Alpro of Nguyen Chi Thanh 2005). We w ill also introduce and analyze the teaching situations with tbe use of this calculator. The knowledge aimed in this situation is the accuracy of the result in a task of approximate calculation.
Keywords: Teaching and leaming. calculator, software emulator, approximate calculation.